The weedkiller I mentioned is for grass, but it will deal with the thistles whilst leaving the grass in place. Apply it and the rain will wash it into the soil to do it's work. If it doesn't rain within 3 days, water it in, or water it in anyway to speed things up. You might need to repeat once or twice more after a week or so. The thistles will start to die within a few days. The grains of weedkiller are small, so it should be relatively safe with kids around, just carefully follow intstructions, and give them gloves for a few days! The weedkiller will be in the soil/ground not on the plants.
Thistles generally are an annual plant, meaning they set seed and die. What you'll need to do is deal with the seeds as they grow. The key then will be hoeing them out when they are young, and before they set seed. This will take a few seasons and you'll need to be diligent. If the kids are old enough get them to do it.Gardening is a great hobby.